Work

Applying Theorems on b-Metric Spaces to Differential and Integral Equations Through Connected-Image Contractions

Year: 2024

Type: article

Abstract: This paper introduces a new concept of a connected-image set for a mapping, which extends the notion of edge-preserving properties with respect to mapping. We also present novel definitions of connected-image contractions, with a focus on fixed-point theorems involving auxiliary functions in b-metric spaces. The relationships between these mathematical concepts are explored, along with their applications to solving differential and integral equations. In particular, we discuss existence results for solving integral equations and second-order ordinary differential equations with inhomogeneous Dirichlet boundary conditions, as well as theorems related to contractions of the integral type.

Source: Mathematics

DOI: 10.3390/math12243955

Authors: Khuanchanok Chaichana, Kanyuta Poochinapan, Teeranush Suebcharoen, Phakdi Charoensawan

Institutions: Centre of Excellence in Mathematics, Ministry of Higher Education, Science, Research and Innovation, Chiang Mai University

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funders: Chiang Mai University, Ministry of Higher Education, Science, Research and Innovation, Thailand